#### Answer

$x_{1}= \sqrt{11}i$ and $x_{2}= -\sqrt{11}i$

#### Work Step by Step

Given $x^2+11=0$
$a=1,\ b=0,\ c=11$
Using the quadratic formula: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} , $ we have:
$\dfrac{-0\pm \sqrt{0^2-4\times 1\times 11}}{2\times 1} = \dfrac{\pm \sqrt{-44}}{2} = \pm \dfrac{ \sqrt{44}i}{2} = \pm \dfrac{ 2\sqrt{11}i}{2} = \pm \sqrt{11}i$
Therefore the solutions are: $x_{1}= \sqrt{11}i$ and $x_{2}= -\sqrt{11}i$